Spotlight SAR
Synthetic aperture radar (SAR) uses moving sensors to form a large synthetic aperture that improves a resolution of an acquired image. In spotlight mode, the pulses emitted by the sensors are steered as a beam to always illuminate a single relatively small area (spot) of interest using pulses transmitted at uniform time intervals. Received signals are used to produce a significantly higher imaging resolution compared to physical aperture arrays, or strip-map mode synthetic arrays. The received signals are also known as echoes or reflections. The received signals that are measured have a complex waveform when compared with the pulses.
However, there is a tradeoff between imaging resolution and coverage. Compared to strip-map mode SAR, conventional spotlight mode cover a much smaller area because of its high sampling rate requirement and restrictions on its beam geometry. This is contrasted with strip-mode SAR where the beam is not steered.
Compressive Sensing
Compressive sensing (CS) is frequently used in sensing applications, including radar imaging. CS enables signal acquisition and accurate reconstruction using a significantly smaller number of measurements compared to the Nyquist rate. The rate reduction is due to randomized measurements, improved signal models, and non-linear reconstruction procedures.
Although CS significantly improves radar and radar imaging systems, a number of challenges still exist in applying CS to radar imaging, such as developing appropriate sparsity models of radar images, and managing computational complexity.
FIG. 1 generally shows conventional spotlight SAR imaging using a linear mono-static array. To image a scene 101, an array of sensors moves along a path 102. Pulses are transmitted at a uniform pulsing rate. Received signals are used to image the reflectivity of the scene.
In spotlight mode, the beam of pulses is steered such that the main lobe of the pulse beam is directed at the center 103 of the area. Each reflection from the area is effectively a convolution of the pulse with the reflectivity of the area covered by the pulse. Thus, the data acquisition process can be modeled as a linear systemy=Φx+n,  (1)where y denotes the received signals, x denotes the reflectivity of the scene, Φ models an array acquisition function of the array parameters, and n is noise.
The goal of the image formation process is to determine the reflectivity x from the received signals y given the acquisition function Φ. In other words, an inverse problem is solved. If the acquisition function Φ is invertible, then an obvious choice would be to use the inverse or the pseudoinverse † of Φ to determine x as{circumflex over (x)}=Φ†y.  (2)
However in practical SAR systems, the acquisition function Φ is generally difficult to model accurately, and the inversion can be computationally complex. Typically, array image formation is achieved using well known procedures, such as a chirp-scaling procedure, or a wave-number procedure, which approximates the inversion.
U.S. Pat. No. 7,973,703 describes an SAR system operating in stripmap mode that reduces the number of pulses by randomly removing some of the pulses to form an image. The reduction introduces blur describes in terms of sidelobes of a main beam.